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A228287 Smallest value of z in the minimal value of x + y*z, given x + y*z = n (where x, y, z are positive integers). 3
1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 2, 3, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,7

COMMENTS

If there are multiple triples (x, y, z) for which xy + z = n and x + yz is minimized, consider the triple with smallest z. I.e., this sequence illustrates the smallest z needed to minimize x + yz.

For n = 215 the triples (53, 4, 3) and (35, 6, 5) both give the minimal value of x + yz = 65. Thus a(215) = 3.

LINKS

Table of n, a(n) for n=2..88.

MAPLE

A228287 := proc(n)

    local a, x, y, z, zfin ;

    a := n+n^2 ;

    zfin := n ;

    for z from 1 to n-1 do

        for x in numtheory[divisors](n-z) do

            y := (n-z)/x ;

            if x+y*z < a then

                a := x+y*z ;

                zfin := z ;

            end if;

        end do:

    end do:

    return zfin;

end proc: # R. J. Mathar, Sep 02 2013

CROSSREFS

Cf. A228286.

Sequence in context: A184348 A307614 A242481 * A213636 A192393 A184303

Adjacent sequences:  A228284 A228285 A228286 * A228288 A228289 A228290

KEYWORD

nonn

AUTHOR

Andy Niedermaier, Aug 19 2013

STATUS

approved

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Last modified September 29 18:27 EDT 2020. Contains 337432 sequences. (Running on oeis4.)